Adding/Subtracting Rational Numbers

• Must have a common denominator!

• Once you have a common denominator, you add/subtract the numerator.

Reviewing parts of a fraction

• Numerator = the top number

• Denominator = the bottom number

Adding fractions with a common denominator

• Add the numerators

• Keep the denominators the same

Adding fractions with different denominators

• Multiply the denominators (to get a common denominator - QCD)

• Multiply the numerator of the first fraction by the opposite denominator

• Multiply the numerator of the second fraction by the opposite denominator

Find the LCM of 21 and 7
21: 21, 42, 63
7: 7, 14, 21, 28
The LCM is 21. Therefore both fractions with have the same denominator which is 21.

• denominators must be equal

• if not, convert using LCM

• when done, simplify using GCF​

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Demoninators must be the same in order to begin!

Adding and subtracting fractions

Adding and Subtracting Rational Numbers

• 1. In order to add or subtract fractions, they must have a common denominator

• 2. The lowest common denominator is the smallest number that is a multiple of all of the denominators

Adding and Subtracting Rational Numbers

• 3. Once the lowest common denominator is found, rewrite all of the fractions as equivalent fractions with that denominator

• 4. Then add (or subtract) numerators, and keep the common denominator

Adding Rational Expressions with the Same Denominator

• 1. if the denominators of the expressions you are trying to add are the same, simply add the numerators and keep the common denominator

• Simplify the numerator by combining like terms

• Factor the numerator and denominator to see if the expression can be reduced

Adding or Subtracting Rational Expressions with Different Denominators

• 1. Before you can combine rational expressions, they must have a common denominator

• 2. Check to see if the smaller denominator is a factor of the larger denominator

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Adding and Subtracting Rational Expressions with Different Denominators

• 3. If one denominator appears as a factor in another denominator, you don't have to repeat that expression in the common denominator

• 4. The lowest common denominator must contain factors that appear in all the denominators

Adding or Subtracting Rational Expressions with Different Denominators

• 5. Once you have decided upon the common denominator, rewrite each expression as an equivalent fraction with the new denominator

• 6. Simplify by combining like terms in the numerator

• 7. Factor the numerator and denominator

• 8. Reduce by canceling like terms.